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Lecture Event
SFB Colloquium Representation Stability (Research Project C1 and C3)
Prof. Benson Farb (University of Chicago)
7 Jan 2014, 16:00 – 18:00


Representation stability: a user's guide
Prof. Benson Farb (University of Chicago)
7 Jan 2014, 16:00 – 16:45

``Representation stability'' refers to a phenomenon discovered a few years ago by Church-Farb that seems to occur all over mathematics; it was developed into a powerful theory with Ellenberg. One simple application gives results such as: the sequence of vector spaces $V_n$ has dimension equal to a polynomial $P(n)$ for $n$ large enough. A common application is to the fixed degree (co)homology of a sequence of spaces $X_n$.
This has been applied to examples in algebraic topology (configuration spaces), algebraic geometry (moduli spaces of surfaces with n marked points, spaces of polynomials on rank varieties), number theory (cohomology of congruence subgroups), algebraic combinatorics (co-invariant algebras), and several other areas. In most cases nothing is known about the actual dimension of $V_n$, but this is now reduced in principle to a finite problem.
The purpose of this talk will be explain to workers in different areas what this theory can do for them, and how they can apply it.

Lecture Events 2014